Yes, cold windows become very brittle whereas warm windows have a degree of elasticity in them that makes them withstand birdstrikes better. On the 777 we always have them on and the system automatically turns them on at the beginning of a flight and off at the end. On older aircraft you have to manually turn them on or off.

One of the most common problems with windshield heat is thermal shocking. Most manual systems had a two position switch; the first position turned the heat on at a low level to gradually warm the windshield up; the second position would bring the windshield up to it normal operating temperature. A lot of people (crews and mechanics) would turn the windshield heat to the high position and, in turn, reduce the windshield's life.
Later windshield heat controllers would ramp up the windshield temperature gradually and thus improved, greatly, the windshield's reliability.
If you look in one corner of the windshield, you will see the electrical grid that is the electrical connection from the power source to the windshield, usually there are two such grids, so if one goes out (which they do), the second grid provides a backup and allows use of the windshield for a longer period.
The windshield has a conductive layer between the glass and acrylic plies that heats the unit.

Yes the window is warm to the touch. A normal temperature is 110deg F.
The systems have thermostats which keep the window from overheating so unless there's a malfunction (not uncommon) there's no danger to the window on the ground.

One may educate the ignorance from the unknowing but stupid is forever. Boswell; ca: 1533